Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
// template.cpp {{{
#include <bits/stdc++.h>
using namespace std;

using lint = long long;
#define reps(i, a, n) for (lint i = (a); i < (lint)(n); ++i)
#define rep(i, n) reps(i, 0, n)
struct pre_{pre_(){cin.tie(0);ios::sync_with_stdio(0);}} pre__;
// }}}

const int INF = 1e9 + 9;

signed main() {
  int n;
  cin >> n;
  vector<int> t(n);
  rep(i, n) cin >> t[i];

  int num = -INF, den = INF;
  int a, b;


  rep(i, n) rep(j, n) {
    if (i == j) continue;
    if (t[i] - t[j] > 0 && t[i] - t[j] < den) {
      a = t[i];
      b = t[j];
      den = t[i] - t[j];
    }
  }

  rep(i, n) rep(j, n) {
    if (i == j) continue;
    if (t[i] == a || t[i] == b || t[j] == a || t[j] == b) continue;
    if (t[i] + t[j] > num) {
      num = t[i] + t[j];
    }
  }

  double res = (double)num / (double)den;

  num = -INF;
  den = INF;
  rep(i, n) rep(j, n) {
    if (i == j) continue;
    if (t[i] + t[j] > num) {
      a = t[i];
      b = t[j];
      num = t[i] + t[j];
    }
  }

  rep(i, n) rep(j, n) {
    if (i == j) continue;
    if (t[i] == a || t[i] == b || t[j] == a || t[j] == b) continue;
    if (t[i] - t[j] > 0 && t[i] - t[j] < den) {
      den = t[i] - t[j];
    }
  }
  cout << fixed << setprecision(10) << max(res, (double)num / (double)den) << endl;
}